This is something that's haunted me for a long time. I used to skip doing presentations in school and take a grade of zero on the assignment, because I didn't want to go up in front of the class and turn beet red. I truly believe that my social anxiety wouldn't be half as bad if I didn't blush. I have read numerous success stories for this issue though, and that gives me hope.
From what I've read and what I've personally experienced, it seems like the best solution (aside from medication or surgery) is to stop caring so much about it. You just need to accept the fact that you are going to blush sometimes and not judge yourself so harshly for it. The fact is, people don't really care if you blush. They might tease you about it, but no one worth your time is going to hate you because you blush. Yes, it is possible that someone may think less of you if they see you blush. But there's also a million other things that people could think less of you for doing. If I could get rid of my blushing, I would probably just find something else about myself to be insecure about.
That previous paragraph sounds good on paper, but when I go out in public, the terror of blushing in front of others always returns. I get so depressed about this, because I can't imagine ever living a normal, happy life as a chronic blusher. Here's an example, what if I get married one day and I have to stand there at the alter with hundreds of people smirking as they watch me turn beet red. Horrifying to think about. I've read about this therapist named Jonathan Berent who claims to have cured a lot of chronic blushers. I'm thinking of contacting him in the future to see if he can help me.